Suppose In = n² - n cos(nn) when n = N. Mark all of the statements that are true when working in the universe of the extended real numbers. lim inf = -∞ 72-00 lim inf n = 2 72-00 lim sup n = ∞ 11-700 lim inf n = 0 721-00 lim n = ∞ 11-00

Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: Show that if x, y are rational numbers, then x + y and xy are rational numbers.

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Q: Show and Sim 218 Iim 276 2²+1 2²+3 2 2-6 2 20 -1

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Q: find lim (-5) h-->0 does not exist O -5 O none of these answers

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Q: x' - 4x? – 9x+36 lim b) x - x-12 x-3 e* -e* – 2x lim c) x- sin x

A: limx→-3x3-4x2-9x+36x2-x-12=limx→-3x2x-4-9x-4x2-4x+3x-12=limx→-3x2-9x-4xx-4+3x-4=limx→-3x2-32x-4x-4x+…

Q: Let m e Z+. Show that =m is an equivalence relation on Z. Prove that for any integer a,

A: Equivalence relation

Q: lim 81x √16x2 4x

A: The given expression is limx→∞16x24x. We have to obtain the limit of the given expression.

Q: Give a de proof that lim (2√x - 4) = -3

A: Details attached in step 2. The answer is typeset in LaTEX.

Q: theorem Every Ving Can be imbeobling în aving with

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Q: 4x 4 lim,-1* - x-1 In x 4 3 5 1 O 2

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Q: In(1+ 3x²) lim ex -1

A: Given that:  lim(x tands to 0) [ln(1+3x2)/ex -1] Here i attached solution of this question.

Q: 1 lim E n→ 00 i=1 'n² + i?

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Q: Calculate lim where an 2". an+1 n00 an

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Q: Find Vr+4-2 lim 0 O 1/4 1/3 O 1/2 None of these

A: given equation is    limx-->0  [√(x+4) - 2] / x   * L- hospital rule  if limx-->0  f(x) / g(x)…

Q: the equasion y=5x+80 and y=10x+60 form a linner equasion in two veriables. Using anymethod to solve…

A: given equations are, y=5x+80 and y=10x+60

Q: 2n 10. Prove that 31 (5 - 1) for every integer n 2 0.

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Q: Suppose a and b are positive real numbers and n is a natural number with n 2 2. (a) Use the…

A: Let a and b are positive real numbers and n is a natural number with n≥2. Use the difference of…

Q: -2x-8 x - 4 (ь) lim O 0° O 100 O c0 O o.00 O c0 - 00 O not indeterminate

A: Given,  limx→∞x2-2x-8x-4  We have to find the form of the limit.

Q: Find the following limit. √√x-4√√x 8%√x+4√√x lim 8118 lim 8118 5√x-4√x 8√x +4√x (Simplify your…

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Q: lim (1+ 00+u Select one: ○ True ○ False = ex n

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Q: d) lim (xe”* +1)/ x->0*

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Q: Underline the domain and then write the negation of the following For all real numbers x, if sin(x)…

A: We know the sin function very well. Graph of the function is  Since the sin(x) is periodic and we…

Q: 2²+3z+2 limz→-1-I-2 Answer: -1/3 (4+z)² –16 lim,→0° Answer: 8 2²+12–4 lim,→2 I-2 Answer: 1/2

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Q: e* - 1 lim VI+x -1 +х — X0

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Q: Which of the following is an oblique asymptote of 0 يع | من O 3 O 814 x 3 4 - - I + Y = 1 4 13 Y 4…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: How can you write any real power of x as a power of e? Are there any restrictions on x? How does…

A: According to the given information it is required to write any real power of x as a power of e.So,…

Q: Suppose the sequence of numbers o, ₁,...,,... satisfies the difference equation 2k+1=0k+ where a and…

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Q: The value of (* +5)(* +1)( - 1) lim * - 1 is O 20 O 6 O 12 O 2 O 72 30

A: The limit of a function need not be the functional value at that point. Consider a rational function…

Q: Which of the following is not an asymptote of * 4x² y = x²-9 Ox=3 O y = -4 Oy=4 O X=-3 ?

A: To find Which of the given is  not an asymptote of y.